Can I include member of political group in resume?

It's for an internship, not a job. I'm a member of the Young Democrats at my school. I would be adding it alongside a couple of other random clubs that I'm in. Also feel free to list anything else that I could put in an internship resume, but not a job resume.

I might list my SF members status if I ever need a resume again. I'll also put "If you are a Republican this interview is over. I don't care what you do with your time but don't waste mine" at the bottom of the page.

You take a risk that the person reviewing your resume is a Republican and wouldn't hire you exactly for that reason. I was in a similar situation in college at one point. I had no interesting extra-curricular activities or related work experience. So I created some. I went out and made the "_______ University Review of Literature and the Arts". I filled out a form to have the organization University approved, which made it listed on the University web page. I made exactly one issue filled with mostly papers I had written for English classes. It cost about $25 to have a copy printed up by the local Pinter. I made a reasonably good looking web site for the club and made myself Editor in Chief. I then put this down on my resume. Nowadays you could probably do this entirely on the internet and not have to spend a penny.

Only if you have a leadership or active position in the campus group and can describe it without referencing the political affiliation. For example, "Leadership position in a major campus political club." Otherwise you risk alienating yourself. Make the focus what you accomplished and not your political affiliation.